2, a periodic function with a period of 2.

3. Title customization function.

4, f(x-a)=f(a-x), a is a constant and a function with a as the symmetry axis.

5, no, one is a periodic function and the other is a symmetric function.

By the way, if you can't recite it, you'd better draw less because the more you draw, the more confused you get.

Several principles I have summarized.

F( 1-x)=f( 1+x) is a symmetric function because the independent variables 1-x and 1+x are symmetric about the straight line x= 1 on the x axis, and the function values are the same.

F(x)=f(x+2) and f(x)=f(x-2) are periodic functions, because the corresponding value of x is the same as that of x-2.

If you see a more complicated formula, you are actually iterating on X and changing it into the form of the first two basic formulas.

As for f (x+y) = f (x) f (y)/f (xy) = f (x) f (y), it is an abstract function completely defined by the proposer himself, so the questions asked will change accordingly. You only need to iterate, draw pictures if necessary, superimpose information in a given domain, and find the value of a particular point. you should

There is another variant, f(x)+f(x-a)=0, so it is actually f(x)=-f(x-a), so try to do it yourself, do an exercise, find out that it should be f(x)=f(x-2a), and then press the above to get the solution.

Finally, using the domain will solve some problems. For example, if f(x) is a function with a period of 2 on the closed interval of (1, 2), then in fact he implicitly tells you that f( 1)=f(2), and so on.

This is my many years of experience in solving problems. I don't know how many questions I have to do before I can use them skillfully, although it is really basic. . . .